The New Exact Value Of (k,r)-arcs And Acceleration Of The Decoding Procedure Of BCH Code

In this thesis, we are concerned with the ( k , r )- arcsin finite projective space and give some new exact values, we also find two ways to accelerate the decoding procedure of BCH code. In addition, we give the solution of how to find the dual base of a fix base in the finite field F over K.Before talking about the problems, we take several papers to introduce some knowledge to projective space and BCH code in order to make preparation for the rest papers.In the first section, we get the theorem that mr (2, q ) = tq + q + 2- tunder the condition that ( q - r )q, t = q + 1- r, r = p n - p m(0≤m≤n)and r≤2/3qby using the knowledge to finite projective space and the two exist theorems. This theorem is also the most important result in the whole paper.In the second section, we give two ways to accelerate the decoding procedure of BCH code. At last, we solve the problem that how to get the dual basis of a fix basis in the finite field F over finite field K.